CN103690333B - A kind of with Biological Strength feedback stiffness variable knee-joint rehabilitation training device and method - Google Patents

Abstract

The invention discloses a variable-stiffness knee joint rehabilitation training device with bio-force feedback and a method thereof, comprising a force-applying structure, a bracket structure, a bio-force signal detection unit, and a control unit, wherein the bio-force signal detection unit includes Surface electrode sheet, signal conditioner, data acquisition and control system, travel switch for position indication, angle sensor, the travel switch is composed of magnetic switch and proximity switch, the control unit includes computer, proportional flow valve, proportional pressure valve, on-off valve , Electromagnetic reversing valve, programmable controller. The present invention can accurately grasp the degree of rehabilitation of the affected knee joint, and use this as a basis to determine the driving force/damping force and the training angle and angular velocity in the rehabilitation training program, which has good scientific nature and avoids the complete reliance on medical personnel in the past The drawbacks of developing a rehabilitation program based on personal experience.

Description

A kind of variable stiffness knee joint rehabilitation training device and method with bio-force feedback

technical field

The invention belongs to the rehabilitation training technology applicable to knee joint injury patients after operation, in particular to a variable stiffness knee joint rehabilitation training device with biological force feedback and a method thereof.

Background technique

The knee joint is an important joint in the human body that undertakes support and movement functions. If the knee joint cannot be effectively exercised in time during the rehabilitation period after injury or medical operation, it is very easy to cause adhesion and muscle atrophy in the knee joint, thereby greatly limiting the movement ability of the knee joint, and even causing serious joint damage. Permanent loss of function. Therefore, modern rehabilitation medicine believes that moderate and effective rehabilitation exercises for the knee joint in time after the operation play a very important role in restoring the function of the knee joint.

The basic requirements for knee rehabilitation equipment mainly focus on two aspects: safety and effectiveness. Safety means that the rehabilitation equipment cannot cause secondary damage to the affected knee during rehabilitation training; effectiveness means that the rehabilitation equipment must not only exercise the flexibility of the joint, but also have the ability to exercise the muscles and ligaments associated with the joint. Necessary stretching exercises and muscle recovery functions. Therefore, the knee joint rehabilitation device should meet the functional requirements of good flexibility and combination of passive and active training.

At present, the knee joint rehabilitation trainers (commonly known as CPM machines, Continuous PassiveMotion) on the market basically adopt the rigid structure drive form of motor + mechanical transmission mechanism, and the motor drives the mechanical transmission mechanism to move, thereby driving the patient's limbs to move (US Patents US6325770B1 and US6221033B1, Chinese Patent 200410006254.0, etc.), this driving method often cannot flexibly apply driving force according to different rehabilitation stages of the affected knee, or change the angle of rehabilitation training, so it is very easy to cause secondary damage to the knee joint. Although many scholars have improved this (Chinese patent 200910031938.9) and added some intelligent control links, the disadvantage of poor safety caused by the rigid drive method has not been fundamentally eradicated. Chinese patent 200410077721.9 uses the Mckibben type pneumatic artificial muscle as the driving element of the knee joint rehabilitation device, which greatly improves the training safety of the rehabilitation device. But this rehabilitator can only implement passive training to patients, and cannot meet the requirements of active training. At the same time, due to the short effective stroke of the Mckibben-type pneumatic muscle, the training angle provided by the rehabilitation training device is small, and the large-angle movement in knee joint rehabilitation training cannot be realized.

In response to the above problems, we proposed a two-way flexible active-passive rehabilitation training device for knee joints (patent number: 201010146310.6), which uses a flexible drive scheme of a rodless cylinder + a large-thrust large-stroke pneumatic flexible drive. A pair of pneumatic flexible actuators are installed in the end resistance, and the flexibility of the actuators is used to ensure the safety of knee joint rehabilitation training in the two directions of knee flexion and knee extension. At the same time, by controlling the different air chambers of the cylinder and the supply/ Exhaust, provide passive training, active training and other different training methods for the affected knee in different rehabilitation processes. However, although the rehabilitation device developed in the early stage can achieve corresponding rehabilitation training, the training force and training angle in different training stages after training are given according to the personal experience of the doctor, which affects the effect of rehabilitation training to a certain extent. .

In order to carry out rehabilitation training for the affected knee more scientifically, it is necessary to scientifically and objectively evaluate the actual rehabilitation status of different rehabilitation objects or the same object at different rehabilitation stages, and formulate a scientific and effective rehabilitation plan based on this, in order to achieve Rehabilitation equipment with the best rehabilitation effect. According to this idea, we have carried out relevant theoretical research work on the detection, processing, evaluation and control methods of the biomechanical signals of the knee-related muscles in the early stage (Nanjing University of Science and Technology Master's Thesis: Knee Joint Rehabilitation Robot Based on Surface EMG Signals Control technology research, author: Wang Shiyun). However, how to implement related technologies and use these researches for rehabilitation training has not yet solved these technical problems in the current published literature.

Contents of the invention

The purpose of the present invention is to provide a variable stiffness knee joint rehabilitation training device with bio-force feedback and its method, which can be applied to rehabilitation training for patients with knee joint injuries after surgery, and can detect in real time the force exerted by the affected knee during the rehabilitation training process The muscle bio-force signal generated by the associated muscles of the knee joint is fed back to determine the driving force during passive training or the variable stiffness control method of damping force during active training, so as to realize the rehabilitation training of the knee joint. Intelligent control, in order to achieve the best rehabilitation training effect.

The technical solution that realizes the object of the present invention is:

A variable stiffness knee joint rehabilitation training device with biological force feedback, including a force application structure and a bracket structure. The force application structure includes a rodless cylinder, a first pneumatic flexible driver, a second pneumatic flexible driver, a sliding pair, and a sliding pair It is composed of a rod and a slider; the bracket structure includes a thigh rod and a calf rod, and a rotating pair is formed between the calf rod and the thigh rod; it also includes a bio-force signal detection unit and a control unit, wherein the bio-force signal detection unit includes surface electrodes , signal conditioner, data acquisition and control system, travel switch for position indication, angle sensor, the travel switch is composed of magnetic switch and proximity switch, the control unit includes computer, proportional flow valve, proportional pressure valve, on-off valve, electromagnetic switch Directional valve, programmable controller;

The first pneumatic flexible driver and the second pneumatic flexible driver are each connected to a proportional flow valve, the two air ports of the rodless cylinder are respectively connected to a proportional flow valve, each proportional flow valve is connected to a proportional pressure valve, and each proportional pressure valve is connected to One on-off valve, each on-off valve is connected with the electromagnetic reversing valve, the proportional flow valve, the proportional pressure valve, the on-off valve and the electromagnetic reversing valve are connected through the air pipe;

The surface electrode sheet is connected with the signal conditioner through the data line, the programmable controller is connected with the computer, the magnetic switch, the proximity switch, the angle sensor, the switch valve and the electromagnetic reversing valve through the data line respectively, and the data acquisition and control system are respectively connected with the computer, The signal conditioner, proportional pressure valve, and proportional flow valve are connected through data lines; more than two magnetic switches are installed in the groove on the outer surface of the cylinder of the rodless cylinder, and the position of the magnetic switch can be placed along the axial direction of the rodless cylinder. The stroke range of the cylinder is adjustable, and it is used to detect the stroke position of the piston of the rodless cylinder during rehabilitation training; proximity switches are set on both sides of the rod of the sliding pair, and the angle sensor is set on the rotating pair between the thigh rod and the calf rod and concentric with the revolving pair.

A variable stiffness knee joint rehabilitation training method with biomechanical feedback is carried out on a two-way flexible knee active-passive rehabilitation training device. During rehabilitation training, surface electrode sheets are attached to the corresponding muscles of the trained lower limbs to Test the biological force generated by muscle contraction during the rehabilitation training process. The biological force signal is transmitted to the signal conditioner through the data transmission line for signal amplification and filtering processing, and the processed signal is collected and processed by the data acquisition and control system. Data acquisition and control The system performs analog/digital conversion on the signal processed by the signal conditioner and then sends it to the computer. The computer extracts the characteristic value RMS of the biological force signal, analyzes and evaluates the strength of the signal, and the data acquisition and control system performs the control instructions issued by the computer. After digital/analog conversion, it is sent to the proportional flow valve and proportional pressure valve. The proportional flow valve and proportional pressure valve control the opening degree of the valve according to the control instructions given by the computer, so as to control the air supply flow and air supply pressure; through programmable The controller controls the opening and closing of the corresponding electromagnets of the on-off valve and the electromagnetic reversing valve to control the opening and closing of the valves, thereby controlling the on-off of the corresponding pneumatic branch, so as to control the process of rehabilitation training.

Compared with the prior art, the present invention has significant advantages: (1) Through the real-time detection of the bio-force signal of the muscles associated with the affected knee joint during the training process, the degree of rehabilitation of the affected knee joint can be accurately grasped and based on this Determining the driving force/damping force and the angle and angular velocity of the rehabilitation training program is scientifically sound and avoids the drawbacks of relying entirely on the personal experience of medical staff to formulate rehabilitation programs in the past. (2) Through the effective control of the air supply pressure, the stiffness of the pneumatic flexible actuator at the end can be gradually controlled to meet the initial requirements of passive training. The rehabilitation device has good flexibility and low stiffness to avoid secondary damage to the affected knee joint However, as the rehabilitation process advances, the requirements for flexibility are continuously weakened, that is, good flexibility is required at the beginning of passive training, and as the rehabilitation process progresses, the requirements for flexibility continue to weaken. (3) According to the recovery degree of muscle strength, by controlling the exhaust flow, the control of the damping force during the active training process can be conveniently realized, so as to achieve the best rehabilitation training effect.

The present invention will be described in further detail below in conjunction with the accompanying drawings.

Description of drawings

Fig. 1 is a schematic diagram of the mechanical structure of the variable stiffness knee joint rehabilitation training device with bio-force feedback of the present invention.

Fig. 2 is a partially enlarged schematic diagram of the E direction of the present invention.

Fig. 3 is a schematic diagram of the composition of the control system of the present invention.

Fig. 4 is a schematic flow chart of using the present invention for rehabilitation training.

Fig. 5 is the variation curve of the dynamic stiffness of the pneumatic flexible actuator with the air supply pressure.

Fig. 6 is a schematic cross-sectional geometric diagram of each layer of the helical elastic tube of the pneumatic flexible actuator.

detailed description

Referring to Fig. 1, Fig. 2 and Fig. 3, the variable stiffness knee joint rehabilitation training device with bio-force feedback of the present invention includes a force application structure, a bracket structure, a bio-force signal detection unit, and a control unit. The force application structure includes a bottom plate 1, a rodless cylinder 2, a slide table 3, a first pneumatic flexible driver 4 (consisting of a spiral elastic tube 33 with a flat initial section), a guide rod 5, and a second pneumatic flexible driver 6 (made of The initial cross-section is composed of a flat spiral elastic tube 33), a fixed bracket 7, a connecting piece 8, a movable bracket 9, and a sliding pair 10; the bracket structure includes a thigh rod 11, a thigh support plate 12, a calf rod 13, and a calf support plate 14. Foot bracket 15, coupling rod 16, T-shaped connector 17, L-shaped rod 18, first adjustment device 19 and second adjustment device 20; the bio-force signal detection unit includes surface electrode sheets 21 (the number is selected according to the needs) ), a signal conditioner 22, a data acquisition and control system 23, a travel switch for position detection and indication (including a magnetic switch 25 and a proximity switch 26, the number of which is selected according to needs), and an angle sensor 27. The control unit includes a computer 24 , a proportional flow valve 28 , a proportional pressure valve 29 , an on-off valve 30 , an electromagnetic reversing valve 31 , and a programmable controller 32 .

The rodless cylinder 2 is fixed on the base plate 1, and two fixed brackets 7 are symmetrically installed on the slide table 3 along the both sides of the stroke direction of the rodless cylinder 2, and guides are installed between the two fixed brackets 7 along the stroke direction of the cylinder. Rod 5, the axis of the guide rod 5 is parallel to the axis of the piston of the rodless cylinder 2, and the second pneumatic flexible driver 6, the movable support 9 and the second A pneumatic flexible driver 4, two pairs of sliding pairs 10 are symmetrically placed on both sides of the center line of the slide table 3 along the stroke direction of the rodless cylinder 2, and the sliding direction of the sliding pair 10 is parallel to the stroke direction of the piston of the rodless cylinder 2; The pair 10 is composed of a rod and a slider, wherein the two ends of the rod are respectively fixed on two fixed brackets 7 , and the slider is fixed on a movable bracket 9 . The movable bracket 9 is fixedly connected with T-shaped connectors 17 on both sides of the direction perpendicular to the cylinder stroke direction, and the two T-shaped connectors 17 are respectively connected with a calf rod 13, and a connecting rod is connected between the two calf rods 13. Rod 16, a foot bracket 15 is installed on the connecting rod 16, a rod member length adjusting device 19 is arranged between the two calf rods 13 and the connecting rod 16, and a calf support plate 14 with soft material is provided between the two calf rods 13 . Between the movable bracket 9 and the T-shaped connector 17, between the calf bar 13 and the thigh bar 11, and between the thigh bar 11 and the L-shaped bar 18, a rotating pair is formed. A thigh supporting plate 12 made of soft material is arranged between the two thigh rods 11 , and two L-shaped rods 18 are respectively fixed on both sides of the base plate 1 , and a rod member length adjusting device 20 is provided.

The first pneumatic flexible driver (4) and the second pneumatic flexible driver (6) are each connected to a proportional flow valve, and the two air ports of the rodless cylinder (2) are respectively connected to a proportional flow valve, and each proportional flow valve (four 1) is connected to a proportional pressure valve, and each proportional pressure valve (four) is connected to an on-off valve, and each on-off valve (four) is connected to the electromagnetic reversing valve (31), the proportional flow valve (28), the proportional pressure valve ( 29), the on-off valve (30) and the electromagnetic reversing valve (31) are connected through air pipes; they constitute 4 pneumatic branches in total, and the compressed air is supplied by the air source device. Two of the pneumatic branches are connected to the two air ports of the rodless cylinder 2 , and the other two pneumatic branches are respectively connected to the first pneumatic flexible driver 4 and the second pneumatic flexible driver 6 .

The surface electrode sheet (21) is connected to the signal conditioner (22) through the data line, and the programmable controller (32) is respectively connected to the computer (24), magnetic switch (25), proximity switch (26), angle sensor (27), The on-off valve (30) and the electromagnetic reversing valve (31) are connected through data lines, and the data acquisition and control system (23) is respectively connected with the computer (24), signal conditioner (22), proportional pressure valve (29), proportional flow valve (28) Connected by a data line; more than two magnetic switches (25) (the number is determined according to the needs) are installed in the groove on the outer surface of the cylinder of the rodless cylinder (2), and the position where the magnetic switch (25) is placed It can be adjusted within the stroke range of the rodless cylinder (2) along the axial direction, and is used to detect the stroke position of the piston of the rodless cylinder (2) during rehabilitation training; on both sides of the rod of the sliding pair (10), close The switch (26) and the angle sensor (27) are arranged at the rotary joint between the thigh bar (11) and the calf bar (13), and are concentric with the rotary joint.

In conjunction with Fig. 4, the variable stiffness knee joint rehabilitation training method with bioforce feedback of the present invention is carried out on the above-mentioned two-way flexible knee joint active-passive rehabilitation training device, and the surface electrode sheet (21) is attached to the The corresponding muscles of the lower limbs are trained to test the biological force generated by muscle contraction during the rehabilitation training process. The biological force signal is transmitted to the signal conditioner (22) through the data transmission line for signal amplification and filtering processing, and is collected and controlled by the data. The system (23) collects and processes the signal, and the data acquisition and control system (23) performs analog/digital conversion on the signal processed by the signal conditioner (22) and sends it to the computer (24), and the computer (24) converts the bio-force signal Extract the characteristic value of the signal (such as extracting the root mean square value RMS of the signal), analyze and evaluate the signal strength, the data acquisition and control system (23) will control the command issued by the computer (24) (for example: judge whether the RMS value exceeds The set threshold, if the RMS value is less than the set threshold, then maintain the last control signal unchanged, on the contrary, if the RMS value is greater than the set threshold, then increase the corresponding control signal voltage value) Analog conversion (for the data acquisition and control system 23 to realize the analog/digital and digital/analog conversion functions, Advantech’s acquisition and control board can be used) and then sent to the proportional flow valve (28) and proportional pressure valve (29), the proportional pressure The valve (29) and the proportional flow valve (28) can control the opening degree of the valve according to the control instruction sent by the computer (24), so as to control the air supply pressure or the air supply flow. For the electromagnetic reversing valve (31) and the switch valve (30), the on-off of the valve electromagnet can be controlled by the programmable controller (32) to control the opening and closing of the valve, so as to control the on-off of the corresponding pneumatic branch circuit.

Below in conjunction with Fig. 1～6, illustrate the specific implementation process of the present invention:

1. Passive training

When the affected limb performs passive knee joint training in the initial stage of rehabilitation, the rodless cylinder 2 and the pneumatic flexible driver in the rehabilitation device are first placed in the initial position. Place the lower limbs to be trained on the bracket structure of the knee joint rehabilitation training device proposed by the present invention and perform necessary fixation, and attach a group of surface electrode sheets 21 to each muscle of the thigh and calf muscle groups in the lower limbs. Turn on each power supply, air source and computer control system. Given initial air supply pressure and air supply flow control signals. At the same time, control the electromagnet on the left side of the electromagnetic reversing valve 31 and the electromagnets of the two switching valves 30 connected to the rodless cylinder 2 to ensure that the P1 port of the rodless cylinder 2 is air-intake, and the P2 port is exhausted (as shown in Figure 3 shown), the sliding table 3 on the rodless cylinder 2 moves to the right as shown in Figure 3, and the connecting rod mechanism composed of the thigh rod 11 and the calf rod 13 in the bracket structure is driven by the sliding table 3 to move, thereby Drive the affected knee joint to perform knee flexion. Carry out knee-bending training; After the magnetic switch 25 detects that the rodless cylinder moves to the right and is in place, the in-place detection signal is sent to the programmable controller 32, and the programmable controller 32 sends the next control command, and the control is connected with the rodless cylinder 2 The electromagnets of the two switching valves 30 are powered off, and the electromagnets of the two switching valves 30 connected to the first pneumatic flexible driver 4 and the second pneumatic flexible driver 6 are energized to ensure that the first pneumatic flexible driver 4 is inflated and the second pneumatic flexible driver is inflated. The pneumatic flexible driver 6 is exhausted, and the slide table 3 continues to move to the right to complete the terminal stroke of the knee-bending training. When the slider in the sliding pair 10 touches the proximity switch 26 arranged at the right end of the rod of the sliding pair 10, or the collected muscle bio-force signal reaches the preset upper threshold, the knee-bending process ends. Proximity switch 26 or computer 24 send detection signal to programmable controller 32, and programmable controller 32 continues to send next control command, controls the electromagnet de-energization of electromagnetic reversing valve 31 left sides, the electromagnet energization of the right side, and first The electromagnets of the two switching valves 30 connected to the pneumatic flexible actuator 4 and the second pneumatic flexible actuator 6 are in the same energized state to ensure that the second pneumatic flexible actuator 6 is inflated, the first pneumatic flexible actuator 4 is exhausted, and the knee extension action begins. When the slide block in the sliding pair 10 touched the proximity switch 26 arranged at the left end of the sliding pair 10 rods, the proximity switch 26 sent a detection signal to the programmable controller 32, and the programmable controller 32 continued to send the next control instruction to control The electromagnets of the two switching valves 30 connected to the first pneumatic flexible driver 4 and the second pneumatic flexible driver 6 are powered off, and the electromagnets of the two switching valves 30 connected to the rodless cylinder 2 are powered on to ensure that the rodless cylinder 2’s P2 port air intake, P1 port exhaust, continue to complete the knee extension action until the magnetic switch 25 detects that the rodless cylinder moves to the left, a training stroke ends, and wait for the next training cycle issued by the programmable controller 32 instructions.

The air supply pressure and air supply flow control signals sent by the computer 24 can control the air supply pressure and flow supplied to the rodless cylinder 2 or the first pneumatic flexible driver 4 during knee flexion training, thereby controlling the driving force and speed. During the knee-bending process, each surface electrode piece 21 detects the electromyographic signal, and the detection signal is amplified and filtered by the signal conditioner 22, and is collected by the data acquisition and control system 23 and transferred to the computer 24 after analog/digital conversion. The software processing system extracts the characteristic value of the collected signal, analyzes and evaluates the strength of the signal (for example: judging whether the RMS value reaches 0.5), and then issues control instructions for the next rehabilitation training. Such a cycle can carry out passive rehabilitation training for the affected knee.

2. Active training

At first each power supply and computer control system are turned on, and the programmable controller 32 sends an initial control command to control the electromagnet on the right side of the electromagnetic reversing valve 31 and the electromagnet energization of all switching valves 30, so as to ensure the operation of the rodless cylinder 2 in the present invention. The right chamber and the second pneumatic flexible driver 6 are in the inflated state, the left chamber of the rodless cylinder 2 and the first pneumatic flexible driver 4 are in the exhaust state, and the rehabilitation device is in the initial position at the left end. Place the lower limbs to be trained on the bracket structure of the knee joint rehabilitation training device proposed by the present invention and perform necessary fixation, and attach a group of surface electrode sheets 21 to each muscle of the thigh and calf muscle groups in the lower limbs. Given initial air supply pressure and air supply flow control signals. Then, the programmable controller 32 sends the next control signal to control the electromagnet on the right side of the electromagnetic reversing valve 31 to be de-energized and the electromagnet on the left side to be energized. The computer 24 sends a control signal to control the air supply pressure of the proportional pressure valve 29 that is connected to the P1 port of the rodless cylinder 2 and connected to the pneumatic flexible driver 4 (the smaller the air supply pressure, the less active force the affected knee will exert during active training). It should be larger, the air supply pressure is 0 in the final stage of rehabilitation training) and the air supply flow rate of the proportional flow valve 28 connected to the P1 port of the rodless cylinder 2 and connected to the pneumatic flexible driver 4 (at this time, the proportional flow valve 28 The valve port is set to the maximum), at the same time, the control signal sent by the computer 24 also controls the size of the exhaust flow of the proportional flow valve 28 connected to the P2 port of the rodless cylinder 2 and connected to the pneumatic flexible driver 6 (the exhaust The greater the flow rate, the smaller the damping force to be overcome during active training; on the contrary, the smaller the exhaust flow, the greater the damping force to be overcome during active training) and connected to the P2 port of the rodless cylinder 2 and the pneumatic flexible drive 6 connected proportional pressure valve 29 (at this moment, the valve port of proportional pressure valve 29 is placed at the maximum). When the affected limb is undergoing active training during the rehabilitation process, it actively uses force to overcome the damping force applied by the rehabilitation device to complete the knee flexion movement, so as to achieve the purpose of exercising the joint-related muscles. During the active training process, each surface electrode sheet 21 detects the electromyographic signal, and the detection signal is amplified, filtered, etc. processed by the signal conditioner 22, collected by the data acquisition and control system 23 and transferred to the computer 24 after analog/digital conversion. The software processing system in the computer extracts the characteristic value of the collected signal and analyzes and evaluates the strength of the signal. If the collected signal reaches the pre-set threshold upper limit, or the magnetic switch 25 detects the in-position signal, then control the electromagnet on the right side of the electromagnetic reversing valve 31 to be energized and the electromagnet on the left side to be de-energized, so as to ensure that the P2 port of the rodless cylinder 2 enters. Gas, P1 port exhaust, the second pneumatic flexible driver 6 intake, the first pneumatic flexible driver 4 exhaust, complete the knee extension action. At the same time, the computer 24 determines and issues control instructions for the next rehabilitation training according to the magnitude of the electromyography signal detected in the previous training cycle. Such a cycle can carry out active rehabilitation training for the affected knee. (Reference: Master Thesis of Nanjing University of Science and Technology: Research on Control Technology of Knee Joint Rehabilitation Robot Based on Surface EMG Signal, Author: Wang Shiyun)

3. Control of variable stiffness of pneumatic flexible actuator

The present invention adopts a pneumatic flexible driver at the end of the knee flexion stroke, and by controlling the air supply pressure of the pneumatic flexible driver, the stiffness of the pneumatic flexible driver can be changed to meet the requirements of variable stiffness of the rehabilitation device when the affected knee has different rehabilitation degrees. The way to change the stiffness is: the dynamic stiffness K _d of the pneumatic flexible actuator is the sum of the static stiffness K _j and the air pressure stiffness K _q .

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}\\ {\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;p</span>}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; N</span>}}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;p\&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; KR</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>\\ {\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; aH</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; aH</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; bH</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; ]</span>\end{array}\right.$

The derivation process of the dynamic stiffness K _d is described below. First define the physical quantity meaning of the following letters:

F is the output force of the pneumatic flexible actuator, p is the air supply pressure, H is the working length of the pneumatic flexible actuator, N is the number of layers of the spiral elastic tube of the pneumatic flexible actuator, and R is the time when the spiral elastic tube of the pneumatic flexible actuator expands to a circular shape , K is the radius change rate of the helical elastic tube of the pneumatic flexible driver, D is the diameter of the guide rod, r ₁ is the inner diameter of the annular contact surface of the helical elastic tube, r ₂ is the outer diameter of the annular contact surface of the helical elastic tube, R' is the actual outer ring radius of the helical elastic tube when the pneumatic flexible driver is working, h is the height of each layer of helical elastic tube, l is the radial contact length of adjacent helical elastic tube layers, is the elongation length correction coefficient of the pneumatic flexible actuator, H _max is the theoretical maximum elongation length of the pneumatic flexible actuator, H _p is the actual maximum elongation length of the pneumatic flexible actuator, λ is the energy conversion efficiency of the pneumatic flexible actuator, n is multi variable index.

Combined with Figure 6, there are:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$

where r ₁ =(D+h)/2

r ₂ =(D+h)/2+l

Another: 2πR'=πh+2l

H=h·N

R'=K·R

At the same time, considering that the pneumatic flexible actuator is affected by the elastic force of the helical elastic tube and the friction force of the outer fiber mesh during the actual elongation process, the pneumatic flexible actuator cannot be extended to the theoretical maximum length H _max , so the elongation length correction is introduced coefficient To correct the theoretical output force model of the pneumatic flexible actuator.

The table below gives an example of the value of K _p for the pneumatic flexible actuator under different input pressures.

input pressure 0.05MPa 0.1MPa 0.15MPa 0.2MPa 0.25MPa 0.3MPa Correction coefficient 1.17 1.07 1.02 1 1 0.98

From this, the mathematical model of the driving force of the pneumatic flexible actuator can be deduced as:

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&lambda;p\&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; p\&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; KR</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;pNKR</span>}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;KR</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

(1) Static stiffness model

When the air supply pressure is constant, the static stiffness of the pneumatic flexible actuator can be expressed as

K _j =dF/dH

Deriving formula (1), the expression of static stiffness can be obtained as:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; p\&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; N</span>}}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{\mathrm{<span\; class="notranslate">\; p\&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; KR</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

(2) Dynamic stiffness model

When the pneumatic flexible actuator is displaced by an external force in a short period of time, the volume of its internal cavity changes, causing a change in the internal gas pressure. When the internal gas has no time to flow relative to the external pipeline, the internal gas pressure of the pneumatic flexible actuator The increase will cause additional restoring force. At this time, the stiffness of the pneumatic flexible actuator is different from the static stiffness. In this case, the stiffness of the pneumatic flexible actuator is called dynamic stiffness.

definition $a={K_p}^2\mathrm{\&lambda;}\frac{{\mathrm{\&pi;}}^2(\mathrm{\&pi;}-2)}{4N},b=-K_p{\mathrm{\&lambda;\&pi;}}^2[\mathrm{KR}(\mathrm{\&pi;}-1)+\frac{\mathrm{D.}}{2}],$

c=λNKRπ ² (πKR+D), then:

F=p(aH ² +bH+c)

Then the static stiffness can also be written as:

K _j =p(2aH+b)(3)

The dynamic force equation of the pneumatic flexible actuator can be expressed as:

F=p(2aH+b)(HH _max )(4)

Deriving formula (4), the expression of dynamic stiffness can be written as:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; aH</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; pa</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; aH</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; )</span>\frac{\mathrm{<span\; class="notranslate">\; dp</span>}}{\mathrm{<span\; class="notranslate">\; dH</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

where the barometric stiffness is defined as:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; qa</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; dp</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}<span\; class="notranslate">\; \&times;</span>\frac{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}{\mathrm{<span\; class="notranslate">\; dH</span>}}<span\; class="notranslate">\; \&times;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; aH</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

That is, the dynamic stiffness is equal to the sum of the static stiffness K _j and the air pressure stiffness K _q .

Assuming that when the pneumatic flexible actuator is subjected to an external force in an instant, the internal gas has no time to exchange with the external gas, according to the ideal gas state equation

pV ⁿ =C(7)

above, is the volume of the working chamber of the pneumatic flexible actuator, is the equivalent cross-sectional area of the pneumatic flexible actuator.

Deriving formula (7), we get:

$\frac{\mathrm{<span\; class="notranslate">\; dp</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; np</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

According to the output force of the pneumatic flexible actuator:

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; aH</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; bH</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&lambda;pN</span>}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

have to $\frac{d\stackrel{\&OverBar;}{A}}{\mathrm{dH}}=(2\mathrm{aH}+b)$

The barometric stiffness is obtained by simplification

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; aH</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; aH</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; bH</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Based on the above, the dynamic stiffness expression of the aerodynamic flexible actuator can be obtained as:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}\\ {\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;p</span>}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; N</span>}}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;p\&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; KR</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>\\ {\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; aH</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; aH</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; bH</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; ]</span>\end{array}\right.$

It can be seen from the dynamic stiffness expression that the parameters affecting the stiffness of the pneumatic flexible actuator are the air supply pressure and various geometric parameters. Therefore, in actual control, the stiffness of the pneumatic flexible actuator can be controlled by controlling the air supply pressure of the pneumatic flexible actuator. Figure 5 is an example of the dynamic stiffness of the pneumatic flexible actuator changing with the change of the air supply pressure.

Claims (1)

1. the stiffness variable knee-joint rehabilitation training device with Biological Strength feedback, comprise force application structure, carrier structure, force application structure comprises Rodless cylinder (2), the first Pneumatic flexible actuator (4), the second Pneumatic flexible actuator (6), sliding pair (10), and sliding pair (10) is made up of rod member and slide block; Carrier structure comprises thigh bar (11), shank bar (13), forms revolute pair between shank bar (13) and thigh bar (11); Characterized by further comprising Biological Strength detecting signal unit, control unit, wherein Biological Strength detecting signal unit comprises travel switch, the angular transducer (27) of surface electrical pole piece (21), signal conditioner (22), data collection and control system (23), position instruction, the trip switch is made up of magnetic switch (25) and proximity switch (26), and control unit comprises computer (24), proportional flow control valve (28), proportional pressure valve (29), switch valve (30), solenoid directional control valve (31), Programmable Logic Controller (32);

Described the first Pneumatic flexible actuator (4), the second Pneumatic flexible actuator (6) respectively connect a proportional flow control valve, two QI KOU of Rodless cylinder (2) connect a proportional flow control valve respectively, each proportional flow control valve connects a proportional pressure valve, each proportional pressure valve connects a switch valve, each switch valve is all connected with solenoid directional control valve (31), and proportional flow control valve (28), proportional pressure valve (29), switch valve (30) are communicated with by trachea with solenoid directional control valve (31);

Surface electrical pole piece (21) is connected by data wire with signal conditioner (22), Programmable Logic Controller (32) is connected by data wire with computer (24), magnetic switch (25), proximity switch (26), angular transducer (27), switch valve (30), solenoid directional control valve (31) respectively, and data collection and control system (23) is connected by data wire with computer (24), signal conditioner (22), proportional pressure valve (29), proportional flow control valve (28) respectively; Plural magnetic switch (25) is installed in the groove of the outer surface of cylinder block of Rodless cylinder (2), the position that magnetic switch (25) is placed can be adjustable in the stroke range of cylinder along Rodless cylinder (2) axis direction, the travel position of the piston of Rodless cylinder (2) during for detecting rehabilitation training; In the rod member both sides of sliding pair (10), proximity switch (26) is set, angular transducer (27) be arranged on thigh bar (11) and and shank bar (13) between rotation vice division chief, and concentric with this revolute pair.